Paper: arXiv 2408.06168

Abstract

We consider an insurance company which faces financial risk in the form of insurance claims and market-dependent surplus fluctuations. The company aims to simultaneously control its terminal wealth (e.g. at the end of an accounting period) and the ruin probability in a finite time interval by purchasing reinsurance. The target functional is given by the expected utility of terminal wealth perturbed by a modified Gerber-Shiu penalty function. We solve the problem of finding the optimal reinsurance strategy and the corresponding maximal target functional via neural networks. The procedure is illustrated by a numerical example, where the surplus process is given by a Cramér-Lundberg model perturbed by a mean-reverting Ornstein-Uhlenbeck process.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper relies heavily on advanced stochastic calculus (Cramér-Lundberg, Ornstein-Uhlenbeck, Gerber-Shiu, HJB) and proposes a novel neural network methodology for a high-dimensional (3D) optimal control problem, indicating high math complexity. However, the sole empirical component is a single numerical example demonstrating proof-of-concept rather than backtest-ready implementation, lacking extensive datasets, statistical metrics, or code, resulting in low empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal: Find Optimal Reinsurance Strategy<br>to Maximize Utility & Minimize Ruin Probability"] --> B["Model Formulation"]
  B --> C["Methodology: Neural Network Approximation"]
  B --> D["Data: Cramér-Lundberg Model +<br>Mean-Reverting OU Process"]
  C --> E["Computational Process: Stochastic Gradient Descent"]
  E --> F["Neural Network learns optimal<br>reinsurance strategy function"]
  F --> G["Outcome: Numerical solution for<br>optimal reinsurance strategy"]
  G --> H["Outcome: Maximal expected utility<br>and minimized ruin probability"]